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# NCERT Solutions for Class 10 Maths, Chapter 1 - Real Numbers

The NCERT Class 9 and 10 Syllabi are interrelated to each other. Therefore, there is no surprise why! The NCERT Class 10 Maths Chapter 1 – Real numbers, is the continuation of Class 9. Having begun its exploration in Class 9, Class 10 – Real numbers chapter starts with two crucial mathematics properties of positive integers viz. The Euclid’s Division Lemma and the Fundamental Theorem of Arithmetic. These properties are followed by Revisiting Irrational Numbers and Revisiting Rational Numbers and Their Decimal Expansions. Let’s take a look at Class 10 Maths, Chapter 1- Real Numbers.

1.1 Introduction

1.2 Euclid’s Division Lemma

1.3 The Fundamental Theorem of Arithmetic

1.4 Revisiting Irrational Numbers

1.5 Revisiting Rational Numbers and Their Decimal Expansions

1.6 Summary

In Class 10 Maths Chapter 1, one will learn -

Section 1.2 – As the name suggests, Euclid’s division algorithm has to do with the divisibility of integers. Basically, Euclid’s division algorithm is a technique to calculate the HCF (Highest Common Factor) of two positive integers.

Section 1.3 – As an alternative to the previous one, the Fundamental Theorem of Arithmetic has to do with the multiplication of positive integers.

Class 10 Real numbers chapter gives you exposure to a wide range of exercises. Besides, it enlightens on the contribution of some of the greatest mathematicians of all time – Muhammad ibn Musa al-Khwarizmi and Carl Friedrich Gauss, also known as the ‘Prince of Mathematicians’ and their theorems that prove to help in solving problems related to real numbers.

Section 1.4 – Again, as the continuation of Class 9 Syllabus, Class 10 Maths Section 1.4 – Revisiting Irrational Numbers proves that ?2, ?3, ?5 and ?p is irrational by using the proof of the Fundamental Theorem of Arithmetic.

Section 1.5 – Revisiting Rational Numbers and Their Decimal Expansions considers or proves that x be a rational number whose decimal expansion terminates.

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